Assume that the spot exchange rate is $S_0(\frac{\text{\$}}{})=$$$0\mathrm{.}7000$ today. The annualized six$-$month

Euro interest rate is $i_{lon}=3\mathrm{.}5\%,$ and the annualized six$-$month dollar interest rate is $i_{\text{\$}}=2\mathrm{.}05\%.$

What is the minimum price that a six$-$month American call option on one Euro with a striking

price of $$0\mathrm{.}6800$ should sell for in a rational market? And what is the minimum price that a

six$-$month American put option on one Euro with a striking price of $$0\mathrm{.}6800$ should sell for in

a rational market?